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A325235 Heinz numbers of integer partitions with Dyson rank 1 or -1.

%I A325235 #6 Apr 13 2019 22:16:59
%S A325235 3,4,10,12,15,18,25,27,28,40,42,60,63,70,88,90,98,100,105,112,132,135,
%T A325235 147,150,168,175,198,208,220,225,245,250,252,280,297,308,312,330,343,
%U A325235 352,375,378,392,420,462,468,484,495,520,528,544,550,567,588,625,630
%N A325235 Heinz numbers of integer partitions with Dyson rank 1 or -1.
%C A325235 Numbers whose maximum prime index and number of prime indices counted with multiplicity differ by 1.
%C A325235 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A325235 FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000145">St000145: The Dyson rank of a partition</a>
%e A325235 The sequence of terms together with their prime indices begins:
%e A325235     3: {2}
%e A325235     4: {1,1}
%e A325235    10: {1,3}
%e A325235    12: {1,1,2}
%e A325235    15: {2,3}
%e A325235    18: {1,2,2}
%e A325235    25: {3,3}
%e A325235    27: {2,2,2}
%e A325235    28: {1,1,4}
%e A325235    40: {1,1,1,3}
%e A325235    42: {1,2,4}
%e A325235    60: {1,1,2,3}
%e A325235    63: {2,2,4}
%e A325235    70: {1,3,4}
%e A325235    88: {1,1,1,5}
%e A325235    90: {1,2,2,3}
%e A325235    98: {1,4,4}
%e A325235   100: {1,1,3,3}
%e A325235   105: {2,3,4}
%e A325235   112: {1,1,1,1,4}
%t A325235 Select[Range[1000],Abs[PrimePi[FactorInteger[#][[-1,1]]]-PrimeOmega[#]]==1&]
%Y A325235 Positions of 1's and -1's in A257541.
%Y A325235 Cf. A001222, A047993, A056239, A061395, A063995, A101198, A106529, A112798, A257990, A263297, A325225, A325233, A325234.
%K A325235 nonn
%O A325235 1,1
%A A325235 _Gus Wiseman_, Apr 13 2019